Chain drop?

When I shift into the small chainring (34T compact double) in front and large cog (25T) in the rear, the chain wants to drop off the chainring to the inside (onto the BB). This started abruptly on my last ride. I do not think it is FD adjustment because the chain does not drop when I shift, but only after I start to put tension on the pedals -- such as starting to climb. Full Dura Ace driveline except for the FSA cranks, and all with very low miles. I am very frustrated. Can anyone give me a tip?

Life is not a journey to the grave with the intention of arriving safely in a pretty and well-preserved body, but rather to skid in broadside, thoroughly used up, totally worn out, and loudly proclaiming, "WOW! WHAT A RIDE!"

Check both derailleurs for adjustment. When you say it wants to fall off the small chainring up front, how is it doing this? If the FD isn't pushing on it - it should just stay put. Without an assist from the FD, I don't understand how this is going on.